Question

Brad wants to open a new savings account. He finds one that returns 3% on his investment each year. Use the variable to write a formula for the final balance after one year. Also b = final balance, x = initial investment, and r = return rate.

Answer 1

Variables: b= final balance, x= initial investment, and r= return rate

• For one year

-b=x(1+r)

• For two years

-b = x(1 + r)(1 + r) = x(1 + r) to the 2nd

• For three years

-b=x(1 + r)to the second(1 + r) = I(1 + r)to the third

• What pattern is forming?

-The final balance each year is equal to the previous year’s final balance multiplied by 1 + r.

• t=time
• Use all the variables to write a formula to find the final balance of the savings account after any number of years.

-b= x(1 + r)to the power of t

• Assume that Brad makes an initial investment of $2,000. Use your formula to find the final balance of the savings account after 15 years.

-b= x(1 + r)to the power of t = $2,000(1 + 0.03)to the 15th ≈ $3,115.93

Explanation:

Answer 2

Return rate, r = 3% = 0.03
x = initial investment
b = final balance

After 1 year, the balance i
b = initial investment + interest
b = x + r*x = (1 + r)*x

Because r = 0.03,
b = 1.03x (after 1 year)